A Lie Group Approach to the Modular Modeling of Kinematically Non-Redundant Parallel Mechanisms

Parallel kinematics manupulators (PKM) are established robotic systems. Yet there is no established modeling approach that takes into account the special kinematics of the (usually structurally identical) limbs. In this paper a modeling approach is proposed that accounts for the special kinematics and topology of PKM. It makes use of modern Lie group formulations for rigid body systems that admits efficient description independent of modeling conventions. A task space formulation is presented that can be directly used for model-based control purposes.